I don't really want to give biased guidance. I studied under a professor for some time who specializes in formal methods, automated analysis, and programming languages, but I can't say I got very far in understanding anything.

There's a way you learn to look at a tool when you have to use it, when it has been formalized, the standard exists, you abide by it, you understand it, agree with it, and can use it, and even may argue for it's usage over a different standard. Then there is the process of the design of formalization, which I think is a much more creative activity. I don't even really consider myself a fraction of the way there, I'm a hobbyist. I don't really get how rigor fits into it.

I have bought a few books and then some connecting these topics (the little schemer, EOPL from freidman, felleisen and wand, SICP, type theory by pierce, automated theorem provers like Coq, the howard curry correspondence). That said, I read pages out of them here and there when I can make the connection on my own. Otherwise, I just program, all the time, I keep up to date with trends, and I try repeatedly figuring out to explain simply that which I have observed to myself, in simpler and simpler ways, until I feel like I get it.

I try very slowly to learn how to read proofs, but sometimes they do become so complex and interconnected with other stuff, that I wonder that I might need n decades of dedicated research and study to figure out how to agree with them.

Sorry if that's not super helpful. The best advice I can give is honest advice, which is, if you have a super active mind and many semi related interests that both distract and guide you, it's going to be hard, confusing, and absurd. But it's fun, and sometimes I feel like I've really made progress.